Once upon a time, I used RW dies to make coin blanks. (Driven by a
kick press. Nothing you’re even going to think about doing with a
hand press.) If you want flat disks, you can special order the dies
without the little spike in the middle. Just tell them you want the
punch ‘flat for blanking’. Or let them know that the disk is your
part, rather than the hole.
There is also a ‘big brother’ to the normal hand punch. It has a
deeper throat, and can take slightly larger dies.
Rather than being the “#5 Junior” the big one is the “XX” punch.
It’ll go up to 17/32".
The big thing about it is that there’s a bench mount for it. So
it’ll lock to your bench, and you can pull down against the bench
with it. MUCH easier. I used it a lot back when I was doing steel
armor, back when dirt was young, and rocks were soft. I wouldn’t say
going through 14ga steel was easy, but it did it, and I was very
happy to have the bench mount.